The Recount process is defined by State RSAs: Post Election Procedure.
The State RSAs are worded to cover State elections, so when secretary of state is shown, Town or School District Clerk can be substituted.
I have included a quick summary provided the the School District clerk.
Who can Request a recount:
For offices, only those names names who appear on the ballot may request a recount. It has to be done by the Friday following the Tuesday election. The cost is defined by RSA 660:2 and is a sliding scale based on the percentage of the vote difference.
For articles a request requires 10 signatures of registered voters, costs $10, and must be done by the close of business the following Monday.
What is the Procedure:
The recount must take place no sooner than 5 days not later than 10 days after receipt of request. All recounts are done by hand. Using the machine is actually prohibited by statute. How long it takes depends on how many ballots were cast, what is being recounted and how it the count is being done.
For an article recount or for a two-candidate race recount we'll sort ballots into piles (Yes/No or Candidate 1/Candidate 2) followed by write-in ballots, blank ballots and "questionable/unclear" ballots. Each pile will then be counted.
Only count cast ballots, but we will open each box to ensure that no cast ballots are in the boxes with uncast and/or cancelled ballots.
For a race with more than two candidates, the count takes longer (and is harder to do) because you have to recount the results for all candidates in the particular race - usually you have one person with a tally sheet and one person who reads (like they do for write-ins and hand counts at the end of the evening.)
The Secretary of State actually counts all the uncast - but we won't do that because we already did at the end of Election night.
Who Counts the Ballots (School District)
The Board of Recount consists of the School Board, the School Moderator and the School Clerk - and the Board will Recount will determine how and if to count any "questionable/unclear" votes.
Who Counts the Ballots (Town)
TBD
Viewing the Process:
The public is allowed to watch from outside the counting area (just like election night) but each candidate is allowed one observer per recount team within the counting area.